A man borrowed some money from a private organization at 5% simple interest per annum. He lent this money to another person at 10% compound interest per annum and made a profit of Rs.26410 in 4 years. The man borrowed:

Rs. 100000

The profit earned by man of Rs. 26410 is the difference between CI and SI of 4 years.

Let the sum is P.

So, CI of 4 years = P(1 + \(\frac{10}{100}\))⁴ - P

                            = P [ (\(\frac{11}{10}\))⁴ - 1]

                            = P [ \(\frac{14641}{10,000}\) - 1]

                            = \(\frac{4641P}{10000}\)

SI of 4 years  = P × \(\frac{5}{100}\) × 4

                        = \(\frac{20P}{100}\)

Now,

CI - SI = \(\frac{4641P}{10000}\) - \(\frac{20P}{100}\)

⇒ [\(\frac{4641-2000}{10000}\)]P = 26410

⇒ \(\frac{2641P}{10000}\) = 26410

⇒ P = 10,00,00